Ascertainment Bias

Ascertainment Bias in a determination of the Primary Sex Ratio:
a classroom demonstration

The Primary Sex Ratio is the ratio of males to females in a population: it is expected to be 1:1. One possible way to count this is to ask a group of people how many brothers and sisters are in their families (including themselves). For example, n = 57 women in Biol2250 were asked to give the counts for their families, with the results as reported above. The ratio of male : female is heavily skewed towards women, almost 2:1 [to be precise, 1.88:1] instead of the expected 1:1.

Why? A census limited to women is guaranteed to include a large number of women (n = 11 out of 57 respondents) that are "only children" (no boys, one girl), and also a number of women from larger all-girl families (a further 12 respondents). Such a census also excludes the reciprocal family types, those with single or all-boy makeup. The result is an ascertainment bias, a mismeasurement of a phenomenon by an error in which the measurement is made. A partial correction is to exclude all respondents with no brothers [first four lines], which in these data would give a male : female ratio of 50:56. A bias in the other direction is expected from a census limited to men.

[Homework: Suppose the classroom measurement of primary sex ratio were done for all undergraduates in the Department of Biology, irrespective of sex. Would you expect a 1:1 ratio? Why or why not? Hint: suppose you did this at the Royal Military College.]

Table & text material ©2016 by Steven M. Carr